I defer to my more electronically inclined friends, but regardless of the tests you did I don't like the look of that burned board. Components on it may have been damaged but haven't quite expired yet. If I was replacing connectors and relaying the headlights, I'd go the whole 9 yards and replace the board.
It looks like the short may have been between those two wires where they entered the connector. Maybe a sloppy assembler left stray wires at the entry point, some conductive debris fell into just the right place, or maybe water? I hate the position of my VIP module in that bay; it used to fill with water leaking inside the cap from the windshield, and that module sits nearly at floor level in there. Fortunately, after 6 years, I've finally stopped the offending leak with Lexel, knock on wood (or fiberglass).
Joel